now :: thesis: for x being object holds
( x in {2,3,4} /\ {1} iff contradiction )

let x be object ; :: thesis: ( x in {2,3,4} /\ {1} iff contradiction )
( x in {2,3,4} /\ {1} iff ( x in {2,3,4} & x in {1} ) ) by XBOOLE_0:def 4;
then ( x in {2,3,4} /\ {1} iff ( ( x = 2 or x = 3 or x = 4 ) & x = 1 ) ) by TARSKI:def 1, ENUMSET1:def 1;
hence ( x in {2,3,4} /\ {1} iff contradiction ) ; :: thesis: verum

end;

hence {2,3,4} /\ {1} = {} by XBOOLE_0:def 1; :: thesis: verum